$CP$ nonconservation in the leptonic sector

In this paper we use an exact method to impose unitarity on moduli of neutrino PMNS matrix recently determined, and show how one could obtain information on $CP$ nonconservation from a limited experimental information. One suggests a novel type of global fit by expressing all theoretical quantities in terms of convention independent parameters: the Jarlskog invariant $J$ and the moduli $|U_{\alpha i}|$, able to resolve the positivity problem of $|U_{e3}|$. In this way the fit will directly provide a value for $J$, and if it is different from zero it will prove the existence of $CP$ violation in the available experimental data. If the best-fit result, $|U_{e3}{|}^2<0$, from M. Maltoni et al., [New J. Phys. 6, 122 (2004)] is confirmed, it will imply a new physics in the leptonic sector.